Azzam al-Ahmad, the deputy prime minister and Fatah member, made his statement to hundreds of teachers on Monday, after they tried to storm government offices in the West Bank city of Ramallah.
"If the economic and national siege on the Palestinian people is not lifted in three months, this government should leave," he said.
Police used batons to push back the teachers at the offices of Ismail Haniya, the Palestinian prime minister and leader of Hamas. Some of the teachers were hit by the police but none was seriously injured.
"The new government should show signs of maturity and responsibility"
Husky, Ottawa, Canada
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The teachers had earlier tried to storm the offices of Naser al-Shaer, the education minister, but he was not there. "Shaer get out," they chanted.
The one-day protest and al-Ahmad's comments put a spotlight on the difficulties the unity government faces in meeting the expectations of Palestinians - who have not received their full wages since Hamas was elected into power last year.
Haniya said last week that Hamas would reassess its options in one to two months if sanctions remained in place. But he did not say that disbanding the government was one of those options.
Salam Fayyad, the Palestinian finance minister, says he plans to start paying partial salaries to government workers at the start of each month, but union leaders say that falls short of the government's promises.
Bassam Zakarneh, chief of the government employee union, has threatened a new round of work stoppages, including another one-day "warning" strike on Wednesday, to demand full wages and back pay.
Hamas formed a unity government with Fatah last month in a bid to end internal fighting and ease a year-old economic embargo.
But tensions between Hamas and Fatah remain high, particularly in the Gaza Strip, and a Western ban on direct aid to the Palestinian Authority remains in place.
Al-Ahmad was meeting in Ramallah with a European delegation when the teachers' protest broke out.
Despite appeals from Fayyad and Abbas, the EU's aid commissioner said last week that EU aid will continue to bypass the Palestinian government until it recognises Israel, renounces violence and abides by interim peace deals as demanded by the Quartet of Middle East mediators and Israel.
Fayyad is counting on receiving at least $55m a month from Arab League members to cover approximately half of the Palestinian Authority's monthly payroll.
His payments would be timed to coincide with "allowances" paid to workers through a European aid programme known as the Temporary International Mechanism.
The European payments are expected to total up to $34m a month.
Together, Fayyad and the Europeans could cover up to 75 per cent of the Palestinian Authority's $115m monthly wage and pension bill, Western diplomats said.